ESTIMATION OF THE KRONECKER COVARIANCE MODEL BY QUADRATIC FORM
提出一种新的二次形式估计量来估计Kronecker乘积协方差模型，在高维情形下具有一致性，并推导了拉格朗日乘子和Wald检验的极限分布，适用于大样本和小样本。
We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension n is large relative to the sample size T ). In particular, the quadratic form estimator is consistent in a relative Frobenius norm sense provided ${\log }^3n/T\to 0$ . We obtain the limiting distributions of the Lagrange multiplier and Wald tests under both the null and local alternatives concerning the mean vector $\mu $ . Testing linear restrictions of $\mu $ is also investigated. Finally, our methodology is shown to perform well in finite sample situations both when the Kronecker product model is true and when it is not true.